<!DOCTYPE html>
<html lang="zh" dir="ltr" class="client-nojs">
<head>
<title>std::comp_ellint_1, std::comp_ellint_1f, std::comp_ellint_1l</title>
<meta charset="UTF-8">
<meta name="generator" content="MediaWiki 1.21.2">
<link rel="shortcut icon" href="../../../../common/favicon.ico">
<link rel="stylesheet" href="../../../../common/ext.css">
<meta name="ResourceLoaderDynamicStyles" content="">
<link rel="stylesheet" href="../../../../common/site_modules.css">
<style>a:lang(ar),a:lang(ckb),a:lang(fa),a:lang(kk-arab),a:lang(mzn),a:lang(ps),a:lang(ur){text-decoration:none}#toc{display:none}.editsection{display:none}
/* cache key: mwiki1-mwiki_zh_:resourceloader:filter:minify-css:7:15cea3ec788a65b5187d4018eed543bf */</style>

<script src="../../../../common/startup_scripts.js"></script>
<script>if(window.mw){
mw.config.set({"wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"cpp/numeric/special_functions/comp_ellint_1","wgTitle":"cpp/numeric/special functions/comp ellint 1","wgCurRevisionId":63268,"wgArticleId":8542,"wgIsArticle":true,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":[],"wgBreakFrames":false,"wgPageContentLanguage":"zh","wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"zh","wgMonthNames":["","1月","2月","3月","4月","5月","6月","7月","8月","9月","10月","11月","12月"],"wgMonthNamesShort":["","1月","2月","3月","4月","5月","6月","7月","8月","9月","10月","11月","12月"],"wgRelevantPageName":"cpp/numeric/special_functions/comp_ellint_1","wgUserVariant":"zh","wgRestrictionEdit":[],"wgRestrictionMove":[]});
}</script><script>if(window.mw){
mw.loader.implement("user.options",function(){mw.user.options.set({"ccmeonemails":0,"cols":80,"date":"default","diffonly":0,"disablemail":0,"disablesuggest":0,"editfont":"default","editondblclick":0,"editsection":0,"editsectiononrightclick":0,"enotifminoredits":0,"enotifrevealaddr":0,"enotifusertalkpages":1,"enotifwatchlistpages":0,"extendwatchlist":0,"externaldiff":0,"externaleditor":0,"fancysig":0,"forceeditsummary":0,"gender":"unknown","hideminor":0,"hidepatrolled":0,"imagesize":2,"justify":0,"math":1,"minordefault":0,"newpageshidepatrolled":0,"nocache":0,"noconvertlink":0,"norollbackdiff":0,"numberheadings":0,"previewonfirst":0,"previewontop":1,"quickbar":5,"rcdays":7,"rclimit":50,"rememberpassword":0,"rows":25,"searchlimit":20,"showhiddencats":0,"showjumplinks":1,"shownumberswatching":1,"showtoc":0,"showtoolbar":1,"skin":"cppreference2","stubthreshold":0,"thumbsize":2,"underline":2,"uselivepreview":0,"usenewrc":0,"watchcreations":0,"watchdefault":0,"watchdeletion":0,
"watchlistdays":3,"watchlisthideanons":0,"watchlisthidebots":0,"watchlisthideliu":0,"watchlisthideminor":0,"watchlisthideown":0,"watchlisthidepatrolled":0,"watchmoves":0,"wllimit":250,"variant":"zh","language":"zh","searchNs0":true,"searchNs1":false,"searchNs2":false,"searchNs3":false,"searchNs4":false,"searchNs5":false,"searchNs6":false,"searchNs7":false,"searchNs8":false,"searchNs9":false,"searchNs10":false,"searchNs11":false,"searchNs12":false,"searchNs13":false,"searchNs14":false,"searchNs15":false,"gadget-MathJax":1,"gadget-ColiruCompiler":1});;},{},{});mw.loader.implement("user.tokens",function(){mw.user.tokens.set({"editToken":"+\\","patrolToken":false,"watchToken":false});;},{},{});
/* cache key: mwiki1-mwiki_zh_:resourceloader:filter:minify-js:7:258d7cd6aa9aa67dee25e01fb6a9e505 */
}</script>
<script>if(window.mw){
mw.loader.load(["mediawiki.page.startup","mediawiki.legacy.wikibits","mediawiki.legacy.ajax"]);
}</script>
<style type="text/css">/*<![CDATA[*/
.source-cpp {line-height: normal;}
.source-cpp li, .source-cpp pre {
	line-height: normal; border: 0px none white;
}
/**
 * GeSHi Dynamically Generated Stylesheet
 * --------------------------------------
 * Dynamically generated stylesheet for cpp
 * CSS class: source-cpp, CSS id: 
 * GeSHi (C) 2004 - 2007 Nigel McNie, 2007 - 2008 Benny Baumann
 * (http://qbnz.com/highlighter/ and http://geshi.org/)
 * --------------------------------------
 */
.cpp.source-cpp .de1, .cpp.source-cpp .de2 {font: normal normal 1em/1.2em monospace; margin:0; padding:0; background:none; vertical-align:top;}
.cpp.source-cpp  {font-family:monospace;}
.cpp.source-cpp .imp {font-weight: bold; color: red;}
.cpp.source-cpp li, .cpp.source-cpp .li1 {font-weight: normal; vertical-align:top;}
.cpp.source-cpp .ln {width:1px;text-align:right;margin:0;padding:0 2px;vertical-align:top;}
.cpp.source-cpp .li2 {font-weight: bold; vertical-align:top;}
.cpp.source-cpp .kw1 {color: #0000dd;}
.cpp.source-cpp .kw2 {color: #0000ff;}
.cpp.source-cpp .kw3 {color: #0000dd;}
.cpp.source-cpp .kw4 {color: #0000ff;}
.cpp.source-cpp .co1 {color: #909090;}
.cpp.source-cpp .co2 {color: #339900;}
.cpp.source-cpp .coMULTI {color: #ff0000; font-style: italic;}
.cpp.source-cpp .es0 {color: #008000; font-weight: bold;}
.cpp.source-cpp .es1 {color: #008000; font-weight: bold;}
.cpp.source-cpp .es2 {color: #008000; font-weight: bold;}
.cpp.source-cpp .es3 {color: #008000; font-weight: bold;}
.cpp.source-cpp .es4 {color: #008000; font-weight: bold;}
.cpp.source-cpp .es5 {color: #008000; font-weight: bold;}
.cpp.source-cpp .br0 {color: #008000;}
.cpp.source-cpp .sy0 {color: #008000;}
.cpp.source-cpp .sy1 {color: #000080;}
.cpp.source-cpp .sy2 {color: #000040;}
.cpp.source-cpp .sy3 {color: #000040;}
.cpp.source-cpp .sy4 {color: #008080;}
.cpp.source-cpp .st0 {color: #008000;}
.cpp.source-cpp .nu0 {color: #000080;}
.cpp.source-cpp .nu6 {color: #000080;}
.cpp.source-cpp .nu8 {color: #000080;}
.cpp.source-cpp .nu12 {color: #000080;}
.cpp.source-cpp .nu16 {color:#000080;}
.cpp.source-cpp .nu17 {color:#000080;}
.cpp.source-cpp .nu18 {color:#000080;}
.cpp.source-cpp .nu19 {color:#000080;}
.cpp.source-cpp .ln-xtra, .cpp.source-cpp li.ln-xtra, .cpp.source-cpp div.ln-xtra {background-color: #ffc;}
.cpp.source-cpp span.xtra { display:block; }

/*]]>*/
</style><style type="text/css">/*<![CDATA[*/
.source-text {line-height: normal;}
.source-text li, .source-text pre {
	line-height: normal; border: 0px none white;
}
/**
 * GeSHi Dynamically Generated Stylesheet
 * --------------------------------------
 * Dynamically generated stylesheet for text
 * CSS class: source-text, CSS id: 
 * GeSHi (C) 2004 - 2007 Nigel McNie, 2007 - 2008 Benny Baumann
 * (http://qbnz.com/highlighter/ and http://geshi.org/)
 * --------------------------------------
 */
.text.source-text .de1, .text.source-text .de2 {font: normal normal 1em/1.2em monospace; margin:0; padding:0; background:none; vertical-align:top;}
.text.source-text  {font-family:monospace;}
.text.source-text .imp {font-weight: bold; color: red;}
.text.source-text li, .text.source-text .li1 {font-weight: normal; vertical-align:top;}
.text.source-text .ln {width:1px;text-align:right;margin:0;padding:0 2px;vertical-align:top;}
.text.source-text .li2 {font-weight: bold; vertical-align:top;}
.text.source-text .ln-xtra, .text.source-text li.ln-xtra, .text.source-text div.ln-xtra {background-color: #ffc;}
.text.source-text span.xtra { display:block; }

/*]]>*/
</style><!--[if lt IE 7]><style type="text/css">body{behavior:url("/mwiki/skins/cppreference2/csshover.min.htc")}</style><![endif]--></head>
<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-cpp_numeric_special_functions_comp_ellint_1 skin-cppreference2 action-view cpp-navbar">
        <!-- header -->
        <!-- /header -->
        <!-- content -->
<div id="cpp-content-base">
            <div id="content">
                <a id="top"></a>
                <div id="mw-js-message" style="display:none;"></div>
                                <!-- firstHeading -->
<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>comp_ellint_1, <span style="font-size:0.7em; line-height:130%">std::</span>comp_ellint_1f, <span style="font-size:0.7em; line-height:130%">std::</span>comp_ellint_1l</h1>
                <!-- /firstHeading -->
                <!-- bodyContent -->
                <div id="bodyContent">
                                        <!-- tagline -->
                    <div id="siteSub">来自cppreference.com</div>
                    <!-- /tagline -->
                                        <!-- subtitle -->
                    <div id="contentSub"><span class="subpages">&lt; <a href="../../../cpp.html" title="cpp">cpp</a>‎ | <a href="../../numeric.html" title="cpp/numeric">numeric</a>‎ | <a href="../special_functions.html" title="cpp/numeric/special functions">special functions</a></span></div>
                    <!-- /subtitle -->
                                                            <!-- bodycontent -->
                    <div id="mw-content-text" lang="zh" dir="ltr" class="mw-content-ltr"><div class="t-navbar" style=""><div class="t-navbar-sep"> </div><div class="t-navbar-head"><a href="../../../cpp.html" title="cpp"> C++</a><div class="t-navbar-menu"><div><div><table class="t-nv-begin" cellpadding="0" style="line-height:1.1em;">
<tr class="t-nv"><td colspan="5"> <a href="../../language.html" title="cpp/language">语言</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../header.html" title="cpp/header">标准库头文件</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../freestanding.html" title="cpp/freestanding"> 自立与有宿主实现</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../named_req.html" title="cpp/named req">具名要求</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../utility.html#.E8.AF.AD.E8.A8.80.E6.94.AF.E6.8C.81" title="cpp/utility">语言支持库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../concepts.html" title="cpp/concepts">概念库</a> <span class="t-mark-rev t-since-cxx20">(C++20)</span> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../error.html" title="cpp/error">诊断库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../utility.html" title="cpp/utility">工具库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../string.html" title="cpp/string">字符串库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="https://zh.cppreference.com/w/cpp/container" title="cpp/container">容器库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../iterator.html" title="cpp/iterator">迭代器库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../ranges.html" title="cpp/ranges"> 范围库</a> <span class="t-mark-rev t-since-cxx20">(C++20)</span> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../algorithm.html" title="cpp/algorithm">算法库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../numeric.html" title="cpp/numeric">数值库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../io.html" title="cpp/io">输入/输出库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../locale.html" title="cpp/locale">本地化库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../regex.html" title="cpp/regex">正则表达式库</a> <span class="t-mark-rev t-since-cxx11">(C++11)</span> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../atomic.html" title="cpp/atomic">原子操作库</a> <span class="t-mark-rev t-since-cxx11">(C++11)</span> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../thread.html" title="cpp/thread">线程支持库</a> <span class="t-mark-rev t-since-cxx11">(C++11)</span> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../filesystem.html" title="cpp/filesystem">文件系统库</a> <span class="t-mark-rev t-since-cxx17">(C++17)</span> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../experimental.html" title="cpp/experimental">技术规范</a> </td></tr>
</table></div><div></div></div></div></div><div class="t-navbar-sep"> </div><div class="t-navbar-head"><a href="../../numeric.html" title="cpp/numeric">数值库</a><div class="t-navbar-menu"><div><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"> <a href="../math.html" title="cpp/numeric/math">常用数学函数</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../special_functions.html" title="cpp/numeric/special functions">数学特殊函数</a> <span class="t-mark-rev t-since-cxx17">(C++17)</span> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../constants.html" title="cpp/numeric/constants">数学常数</a> <span class="t-mark-rev t-since-cxx20">(C++20)</span></td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../fenv.html" title="cpp/numeric/fenv">浮点环境</a> <span class="t-mark-rev t-since-cxx11">(C++11)</span> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../complex.html" title="cpp/numeric/complex">复数</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../valarray.html" title="cpp/numeric/valarray">数值数组</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../random.html" title="cpp/numeric/random">伪随机数生成</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../ratio.html" title="cpp/numeric/ratio">编译时有理数算术</a> <span class="t-mark-rev t-since-cxx11">(C++11)</span> </td></tr>
<tr class="t-nv-h2"><td colspan="5">数值算法</td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../gcd.html" title="cpp/numeric/gcd"><span class="t-lines"><span>gcd</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../lcm.html" title="cpp/numeric/lcm"><span class="t-lines"><span>lcm</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span></span></div></div></td></tr>
<tr class="t-nv-h2"><td colspan="5">插值</td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../midpoint.html" title="cpp/numeric/midpoint"><span class="t-lines"><span>midpoint</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../lerp.html" title="cpp/numeric/lerp"><span class="t-lines"><span>lerp</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv-h2"><td colspan="5">通用数值运算</td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../../algorithm/iota.html" title="cpp/algorithm/iota"><span class="t-lines"><span>iota</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../../algorithm/accumulate.html" title="cpp/algorithm/accumulate"><span class="t-lines"><span>accumulate</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../../algorithm/inner_product.html" title="cpp/algorithm/inner product"><span class="t-lines"><span>inner_product</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../../algorithm/adjacent_difference.html" title="cpp/algorithm/adjacent difference"><span class="t-lines"><span>adjacent_difference</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../../algorithm/partial_sum.html" title="cpp/algorithm/partial sum"><span class="t-lines"><span>partial_sum</span></span></a></div></div></td></tr>
<tr class="t-nv-h2"><td colspan="5">位操作</td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../bit_cast.html" title="cpp/numeric/bit cast"><span class="t-lines"><span>bit_cast</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../has_single_bit.html" title="cpp/numeric/has single bit"><span class="t-lines"><span>has_single_bit</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../bit_ceil.html" title="cpp/numeric/bit ceil"><span class="t-lines"><span>bit_ceil</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../bit_floor.html" title="cpp/numeric/bit floor"><span class="t-lines"><span>bit_floor</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../bit_width.html" title="cpp/numeric/bit width"><span class="t-lines"><span>bit_width</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../rotl.html" title="cpp/numeric/rotl"><span class="t-lines"><span>rotl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../rotr.html" title="cpp/numeric/rotr"><span class="t-lines"><span>rotr</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../countl_zero.html" title="cpp/numeric/countl zero"><span class="t-lines"><span>countl_zero</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../countl_one.html" title="cpp/numeric/countl one"><span class="t-lines"><span>countl_one</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../countr_zero.html" title="cpp/numeric/countr zero"><span class="t-lines"><span>countr_zero</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../countr_one.html" title="cpp/numeric/countr one"><span class="t-lines"><span>countr_one</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../popcount.html" title="cpp/numeric/popcount"><span class="t-lines"><span>popcount</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../../types/endian.html" title="cpp/types/endian"><span class="t-lines"><span>endian</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
</table></div><div></div></div></div></div><div class="t-navbar-sep"> </div><div class="t-navbar-head"><a href="../special_functions.html" title="cpp/numeric/special functions">数学特殊函数</a><div class="t-navbar-menu"><div><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv-col-table"><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/assoc_laguerre.html" title="cpp/numeric/special functions/assoc laguerre"><span class="t-lines"><span>assoc_laguerre</span><span>assoc_laguerref</span><span>assoc_laguerrel</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/assoc_legendre.html" title="cpp/numeric/special functions/assoc legendre"><span class="t-lines"><span>assoc_legendre</span><span>assoc_legendref</span><span>assoc_legendrel</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/beta.html" title="cpp/numeric/special functions/beta"><span class="t-lines"><span>beta</span><span>betaf</span><span>betal</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><strong class="selflink"><span class="t-lines"><span>comp_ellint_1</span><span>comp_ellint_1f</span><span>comp_ellint_1l</span></span></strong></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/comp_ellint_2.html" title="cpp/numeric/special functions/comp ellint 2"><span class="t-lines"><span>comp_ellint_2</span><span>comp_ellint_2f</span><span>comp_ellint_2l</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/comp_ellint_3.html" title="cpp/numeric/special functions/comp ellint 3"><span class="t-lines"><span>comp_ellint_3</span><span>comp_ellint_3f</span><span>comp_ellint_3l</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/cyl_bessel_i.html" title="cpp/numeric/special functions/cyl bessel i"><span class="t-lines"><span>cyl_bessel_i</span><span>cyl_bessel_if</span><span>cyl_bessel_il</span></span></a></div></div></td></tr>
</table></div></td><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/cyl_bessel_j.html" title="cpp/numeric/special functions/cyl bessel j"><span class="t-lines"><span>cyl_bessel_j</span><span>cyl_bessel_jf</span><span>cyl_bessel_jl</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/cyl_bessel_k.html" title="cpp/numeric/special functions/cyl bessel k"><span class="t-lines"><span>cyl_bessel_k</span><span>cyl_bessel_kf</span><span>cyl_bessel_kl</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/cyl_neumann.html" title="cpp/numeric/special functions/cyl neumann"><span class="t-lines"><span>cyl_neumann</span><span>cyl_neumannf</span><span>cyl_neumannl</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/ellint_1.html" title="cpp/numeric/special functions/ellint 1"><span class="t-lines"><span>ellint_1</span><span>ellint_1f</span><span>ellint_1l</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/ellint_2.html" title="cpp/numeric/special functions/ellint 2"><span class="t-lines"><span>ellint_2</span><span>ellint_2f</span><span>ellint_2l</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/ellint_3.html" title="cpp/numeric/special functions/ellint 3"><span class="t-lines"><span>ellint_3</span><span>ellint_3f</span><span>ellint_3l</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/expint.html" title="cpp/numeric/special functions/expint"><span class="t-lines"><span>expint</span><span>expintf</span><span>expintl</span></span></a></div></div></td></tr>
</table></div></td><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/hermite.html" title="cpp/numeric/special functions/hermite"><span class="t-lines"><span>hermite</span><span>hermitef</span><span>hermitel</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/laguerre.html" title="cpp/numeric/special functions/laguerre"><span class="t-lines"><span>laguerre</span><span>laguerref</span><span>laguerrel</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/legendre.html" title="cpp/numeric/special functions/legendre"><span class="t-lines"><span>legendre</span><span>legendref</span><span>legendrel</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/riemann_zeta.html" title="cpp/numeric/special functions/riemann zeta"><span class="t-lines"><span>riemann_zeta</span><span>riemann_zetaf</span><span>riemann_zetal</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/sph_bessel.html" title="cpp/numeric/special functions/sph bessel"><span class="t-lines"><span>sph_bessel</span><span>sph_besself</span><span>sph_bessell</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/sph_legendre.html" title="cpp/numeric/special functions/sph legendre"><span class="t-lines"><span>sph_legendre</span><span>sph_legendref</span><span>sph_legendrel</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../special_math/sph_neumann.html" title="cpp/numeric/special functions/sph neumann"><span class="t-lines"><span>sph_neumann</span><span>sph_neumannf</span><span>sph_neumannl</span></span></a></div></div></td></tr>
</table></div></td></tr>
</table></div><div></div></div></div></div><div class="t-navbar-sep"> </div></div>
<table class="t-dcl-begin"><tbody>
<tr class="t-dsc-header">
<td> <div>定义于头文件 <code><a href="../../header/cmath.html" title="cpp/header/cmath">&lt;cmath&gt;</a></code>
 </div></td>
<td></td>
<td></td>
</tr>
<tr class="t-dcl t-since-cxx17">
<td> <div><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span>      comp_ellint_1<span class="br0">(</span> <span class="kw4">double</span> k <span class="br0">)</span><span class="sy4">;</span><br>
<p><span class="kw4">float</span>       comp_ellint_1<span class="br0">(</span> <span class="kw4">float</span> k <span class="br0">)</span><span class="sy4">;</span><br>
<span class="kw4">long</span> <span class="kw4">double</span> comp_ellint_1<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> k <span class="br0">)</span><span class="sy4">;</span><br>
<span class="kw4">float</span>       comp_ellint_1f<span class="br0">(</span> <span class="kw4">float</span> k <span class="br0">)</span><span class="sy4">;</span><br>
</p>
<span class="kw4">long</span> <span class="kw4">double</span> comp_ellint_1l<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> k <span class="br0">)</span><span class="sy4">;</span></span></div></td>
<td> (1) </td>
<td> <span class="t-mark-rev t-since-cxx17">(C++17 起)</span> </td>
</tr>
<tr class="t-dcl t-since-cxx17">
<td> <div><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span>      comp_ellint_1<span class="br0">(</span> IntegralType k <span class="br0">)</span><span class="sy4">;</span></span></div></td>
<td> (2) </td>
<td> <span class="t-mark-rev t-since-cxx17">(C++17 起)</span> </td>
</tr>
<tr class="t-dcl-sep"><td></td><td></td><td></td></tr>
</tbody></table>
<div class="t-li1"><span class="t-li">1)</span> 计算 <code>k</code> 的<a href="https://en.wikipedia.org/wiki/Elliptic_integral#Complete_elliptic_integral_of_the_first_kind" class="extiw" title="enwiki:Elliptic integral">第一类完全椭圆积分</a>。</div>
<div class="t-li1"><span class="t-li">2)</span> 接受任意<a href="../../types/is_integral.html" title="cpp/types/is integral">整数类型</a>参数的重载集或函数模板。等价于将参数转型到 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span></span></span> 后的 <span class="t-v">(1)</span> 。</div>
<h3><span class="mw-headline" id=".E5.8F.82.E6.95.B0">参数</span></h3>
<table class="t-par-begin">


<tr class="t-par">
<td>  k
</td>
<td> -
</td>
<td> 椭圆模或离心率（浮点或整数类型值）
</td></tr></table>
<h3><span class="mw-headline" id=".E8.BF.94.E5.9B.9E.E5.80.BC">返回值</span></h3>
<p>若无错误发生，则返回 <code>k</code> 的第一类完全椭圆积的值，即 <span class="t-lc">ellint_1(k,π/2)</span> 。
</p>
<h3><span class="mw-headline" id=".E9.94.99.E8.AF.AF.E5.A4.84.E7.90.86">错误处理</span></h3>
<p>可能报告 <a href="../math/math_errhandling.html" title="cpp/numeric/math/math errhandling"><tt>math_errhandling</tt></a> 中指定的错误。
</p>
<ul><li> 若参数是 NaN ，则返回 NaN 且不报告定义域错误
</li><li> 若 <span class="texhtml" style="white-space: nowrap;">|k|&gt;1</span> ，则可能发生定义域错误
</li></ul>
<h3><span class="mw-headline" id=".E6.B3.A8.E8.A7.A3">注解</span></h3>
<p>不支持 C++17 ，但支持 <a href="../../experimental/special_functions.html" title="cpp/experimental/special functions">ISO 29124:2010</a> 的实现会提供此函数，若实现定义了 <code>__STDCPP_MATH_SPEC_FUNCS__</code> 为至少 201003L 的值，且用户在包含任何标准库头文件前定义了 <code>__STDCPP_WANT_MATH_SPEC_FUNCS__</code> 。
</p><p>不支持 ISO 29124:2010 但支持 TR 19768:2007 (TR1) 的实现，在头文件 <code>tr1/cmath</code> 及命名空间 <code>std::tr1</code> 中提供此函数。
</p><p>此函数的一种实现亦<a rel="nofollow" class="external text" href="http://www.boost.org/doc/libs/1_60_0/libs/math/doc/html/math_toolkit/ellint/ellint_1.html">可用于 boost.math</a>
</p><p>给定重力加速度 <span class="texhtml" style="white-space: nowrap;">g</span> ，及初始角 θ ，则长度为 <span class="texhtml" style="white-space: nowrap;">l</span> 的<a href="https://en.wikipedia.org/wiki/Pendulum_(mathematics)" class="extiw" title="enwiki:Pendulum (mathematics)">钟摆周期</a>等于 <span class="texhtml" style="white-space: nowrap;">4<span class="t-mrad"><span>√</span><span>l/g</span></span>K(sin<span class="t-su">2<br></span>(θ/2))</span> ，其中 <span class="texhtml" style="white-space: nowrap;">K</span> 是 <code>std::comp_ellint_1</code> 。
</p>
<h3><span class="mw-headline" id=".E7.A4.BA.E4.BE.8B">示例</span></h3>
<div class="t-example"><div class="t-example-live-link"><div class="coliru-btn coliru-btn-run-init">运行此代码</div></div>
<div dir="ltr" class="mw-geshi" style="text-align: left;"><div class="cpp source-cpp"><pre class="de1"><span class="co2">#include &lt;cmath&gt;</span>
<span class="co2">#include &lt;iostream&gt;</span>
<span class="kw4">int</span> main<span class="br0">(</span><span class="br0">)</span>
<span class="br0">{</span>
    <span class="kw4">double</span> hpi <span class="sy1">=</span> <a href="../math/acos.html"><span class="kw1337">std::<span class="me2">acos</span></span></a><span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span><span class="br0">)</span><span class="sy2">/</span><span class="nu0">2</span><span class="sy4">;</span>
    <a href="../../io/cout.html"><span class="kw1758">std::<span class="me2">cout</span></span></a> <span class="sy1">&lt;&lt;</span> <span class="st0">"K(0) = "</span> <span class="sy1">&lt;&lt;</span> <a href="../special_math/comp_ellint_1.html"><span class="kw1396">std::<span class="me2">comp_ellint_1</span></span></a><span class="br0">(</span><span class="nu0">0</span><span class="br0">)</span> <span class="sy1">&lt;&lt;</span> <span class="st0">'<span class="es1">\n</span>'</span>
              <span class="sy1">&lt;&lt;</span> <span class="st0">"π/2 = "</span> <span class="sy1">&lt;&lt;</span> hpi <span class="sy1">&lt;&lt;</span> <span class="st0">'<span class="es1">\n</span>'</span>
              <span class="sy1">&lt;&lt;</span> <span class="st0">"K(0.5) = "</span> <span class="sy1">&lt;&lt;</span> <a href="../special_math/comp_ellint_1.html"><span class="kw1396">std::<span class="me2">comp_ellint_1</span></span></a><span class="br0">(</span><span class="nu16">0.5</span><span class="br0">)</span> <span class="sy1">&lt;&lt;</span> <span class="st0">'<span class="es1">\n</span>'</span>
              <span class="sy1">&lt;&lt;</span> <span class="st0">"F(0.5, π/2) = "</span> <span class="sy1">&lt;&lt;</span> <a href="../special_math/ellint_1.html"><span class="kw1417">std::<span class="me2">ellint_1</span></span></a><span class="br0">(</span><span class="nu16">0.5</span>, hpi<span class="br0">)</span> <span class="sy1">&lt;&lt;</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
    <a href="../../io/cout.html"><span class="kw1758">std::<span class="me2">cout</span></span></a> <span class="sy1">&lt;&lt;</span> <span class="st0">"Period of a pendulum length 1 m at 90 degree initial angle is "</span>
              <span class="sy1">&lt;&lt;</span> <span class="nu0">4</span><span class="sy2">*</span><a href="../math/sqrt.html"><span class="kw1329">std::<span class="me2">sqrt</span></span></a><span class="br0">(</span><span class="nu0">1</span><span class="sy2">/</span><span class="nu16">9.80665</span><span class="br0">)</span><span class="sy2">*</span>
                 <a href="../special_math/comp_ellint_1.html"><span class="kw1396">std::<span class="me2">comp_ellint_1</span></span></a><span class="br0">(</span><a href="../math/pow.html"><span class="kw1332">std::<span class="me2">pow</span></span></a><span class="br0">(</span><a href="../math/sin.html"><span class="kw1333">std::<span class="me2">sin</span></span></a><span class="br0">(</span>hpi<span class="sy2">/</span><span class="nu0">2</span><span class="br0">)</span>,<span class="nu0">2</span><span class="br0">)</span><span class="br0">)</span> <span class="sy1">&lt;&lt;</span> <span class="st0">" s<span class="es1">\n</span>"</span><span class="sy4">;</span>
<span class="br0">}</span></pre></div></div>
<p>输出：
</p>
<div dir="ltr" class="mw-geshi" style="text-align: left;"><div class="text source-text"><pre class="de1">K(0) = 1.5708
π/2 = 1.5708
K(0.5) = 1.68575
F(0.5, π/2) = 1.68575
Period of a pendulum length 1 m at 90 degree initial angle is 2.15324 s</pre></div></div> 
</div>
<h3><span class="mw-headline" id=".E5.A4.96.E9.83.A8.E9.93.BE.E6.8E.A5">外部链接</span></h3>
<p><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/CompleteEllipticIntegraloftheFirstKind.html">Weisstein, Eric W. “第一类完全椭圆积分”</a>来自 MathWorld--A Wolfram Web Resource 。
</p>
<h3><span class="mw-headline" id=".E5.8F.82.E9.98.85">参阅</span></h3>
<table class="t-dsc-begin">

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="../special_math/ellint_1.html" title="cpp/numeric/special functions/ellint 1"> <span class="t-lines"><span>ellint_1</span><span>ellint_1f</span><span>ellint_1l</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span></span></div></div>
</td>
<td>  第一类（不完全）椭圆积分 <br> <span class="t-mark">(函数)</span> </td></tr>
</table>

<!-- 
NewPP limit report
Preprocessor visited node count: 4479/1000000
Preprocessor generated node count: 8282/1000000
Post‐expand include size: 126314/2097152 bytes
Template argument size: 24270/2097152 bytes
Highest expansion depth: 20/40
Expensive parser function count: 0/100
-->

<!-- Saved in parser cache with key mwiki1-mwiki_zh_:pcache:idhash:8542-0!*!0!!zh!*!zh!* and timestamp 20200221230013 -->
</div>                    <!-- /bodycontent -->
                                        <!-- printfooter -->
                    <div class="printfooter">
                    来自“<a href="https://zh.cppreference.com/mwiki/index.php?title=cpp/numeric/special_functions/comp_ellint_1&amp;oldid=63268">https://zh.cppreference.com/mwiki/index.php?title=cpp/numeric/special_functions/comp_ellint_1&amp;oldid=63268</a>”                    </div>
                    <!-- /printfooter -->
                                                            <!-- catlinks -->
                    <!-- /catlinks -->
                                                            <div class="visualClear"></div>
                    <!-- debughtml -->
                                        <!-- /debughtml -->
                </div>
                <!-- /bodyContent -->
            </div>
        </div>
        <!-- /content -->
        <!-- footer -->
        <div id="cpp-footer-base" class="noprint">
            <div id="footer">
                        <div id="cpp-navigation">
            <h5>导航</h5>
            <ul><li><a href="https://zh.cppreference.com/w/cpp/numeric/special_functions/comp_ellint_1">Online version</a></li><li>Offline version retrieved 2020-03-14 18:00.</li></ul></div>
                        <ul id="footer-info">
                                    <li id="footer-info-lastmod"> 本页面最后修改于2019年11月29日 (星期五) 07:30。</li>
                                    <li id="footer-info-viewcount">此页面已被浏览过1,434次。</li>
                            </ul>
                    </div>
        </div>
        <!-- /footer -->
        <script>if(window.mw){
mw.loader.state({"site":"loading","user":"missing","user.groups":"ready"});
}</script>
<script src="../../../../common/skin_scripts.js"></script>
<script>if(window.mw){
mw.loader.load(["mediawiki.action.view.postEdit","mediawiki.user","mediawiki.page.ready","mediawiki.searchSuggest","mediawiki.hidpi","ext.gadget.MathJax","ext.gadget.ColiruCompiler"], null, true);
}</script>
<script src="../../../../common/site_scripts.js"></script>
<script type="text/javascript">
var _gaq = _gaq || [];
_gaq.push(['_setAccount', 'UA-2828341-1']);
_gaq.push(['_setDomainName', 'cppreference.com']);
_gaq.push(['_trackPageview']);
</script><!-- Served in 0.758 secs. -->
	</body>
<!-- Cached 20200221230013 -->
</html>